Answer:
0.89417
Step-by-step explanation:
Using the relation to obtain the Zscore :
Z = (x - mean) ÷ standard deviation / sqrt(n)
x = 0.8535
Mean = 0.8565
Standard deviation = 0.0518
Sample size, n = 465
P(x ≤ 0.8535) = (0.8535 - 0.8565) ÷ 0.0518/sqrt(465)
P(x ≥ 0.8535) = - 0.003 / 0.0024021
P(x ≥ 0.8535) = - 1.249
P(Z ≥ - 1.249) = 0.89417
Answer:
The spy must have at the start the amount of $1,024 in order to escape
Step-by-step explanation:
Let
a ------> amount of money that the spy must have at the start to escape
y ----> the remaining money
x ----> the number of guards
In this problem the remaining money is going to be reduced by half, every time the spy passes through a guard, so we can use an exponential function of the form
where
a is the initial value (amount of money at the start)
b is the base
b=(1-r)
r is the rate of decay
In this problem we have
r=50% -----> r=0.50
The value of b is
b=(1-0.50)=0.50
substitute
we know that
In order to escape after the fourth guard the amount of money remaining must be equal to $64
so
For x=4, y=$64
substitute in the equation and solve for a
therefore
The spy must have at the start the amount of $1,024 in order to escape
Answer:
x=151/64 y=9/8 z=-51/32
Step-by-step explanation:
2x+2y+5z- (2x-y+z)=-1-2
3y+4z=-3
2x+2y+5z- (2x+4y-3z)=-1-14
-2y+8z=-15
We have two equations 3y+4z=-3 and -2y+8z=-15 (We get it due to elimination method)
3y+4z=-3 (2)
-2y+8z=-15 (-3)
6y+8z=-6
6y-24z=45
(6y+8z)- (6y-24z)= -6-45
32z=-51
z=-51/32
3y-204/32=-3
3y= -96/32+204/32
3y=108/32
y=36/32=9/8
2x+2*9/8+5*(-51/32)=-1
2x+9/4-255/32=-1
2x+72/32-255/32=-1
2x-183/32=-32/32
2x=151/32
x=151/64
A=43°
B=82°
c=28
1) A+B+C=180°
Replacing A=43° and B=82° in the equation above:
43°+82°+C=180°
125°+C=180°
Solving for C. Subtracting 125° both sides of the equation:
125°+C-125°=180°-125°
C=55° (option B or C)
2) Law of sines
a/sin A=b/sin B=c/sin C
Replacing A=43°, B=82°, C=55°, and c=28 in the equation above:
a/sin 43°=b/sin 82°=28/sin 55°
2.1) a/sin 43°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 43°:
sin 43°(a/sin 43°)=sin 43°(28/sin 55°)
a=28 sin 43° / sin 55°
Using the calculator: sin 43°=0.681998360, sin 55°=0.819152044
a=28(0.681998360)/0.819152044
a=23.31185549
Rounded to one decimal place
a=23.3
2.2) b/sin 82°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 82°:
sin 82°(b/sin 82°)=sin 82°(28/sin 55°)
b=28 sin 82° / sin 55°
Using the calculator: sin 82°=0.990268069, sin 55°=0.819152044
b=28(0.990268069)/0.819152044
b=33.84903466
Rounded to one decimal place
b=33.8
Answer: Option B) C=55°, b=33.8, a=23.3
Answer:
8, 0, -8, -12
Step-by-step explanation:
